TY - JOUR
T1 - Multipartite entanglement and quantum error identification in D -dimensional cluster states
AU - Sudevan, Sowrabh
AU - Azses, Daniel
AU - Dalla Torre, Emanuele G.
AU - Sela, Eran
AU - Das, Sourin
N1 - Publisher Copyright:
© 2023 American Physical Society.
PY - 2023/8
Y1 - 2023/8
N2 - An entangled state is said to be m-uniform if the reduced density matrix of any m qubits is maximally mixed. This is intimately linked to pure quantum error correction codes (QECCs), which allow us not only to correct errors but also to identify their precise nature and location. Here, we show how to create m-uniform states using local gates or interactions and elucidate several QECC applications. We first show that D-dimensional cluster states are m-uniform with m=2D. This zero-correlation-length cluster state does not have finite-size corrections to its m=2D uniformity, which is exact both for infinite lattices and for large enough, but finite, lattices. Yet at some finite value of the lattice extension in each of the D dimensions, which we bound, the uniformity is degraded due to finite support operators which wind around the system. We also outline how to achieve larger m values using quasi-D-dimensional cluster states. This opens the possibility to use cluster states to benchmark errors on quantum computers. We demonstrate this ability on a superconducting quantum computer, focusing on the one-dimensional cluster state, which, as we show, allows us to detect and identify one-qubit errors, distinguishing X, Y, and Z errors.
AB - An entangled state is said to be m-uniform if the reduced density matrix of any m qubits is maximally mixed. This is intimately linked to pure quantum error correction codes (QECCs), which allow us not only to correct errors but also to identify their precise nature and location. Here, we show how to create m-uniform states using local gates or interactions and elucidate several QECC applications. We first show that D-dimensional cluster states are m-uniform with m=2D. This zero-correlation-length cluster state does not have finite-size corrections to its m=2D uniformity, which is exact both for infinite lattices and for large enough, but finite, lattices. Yet at some finite value of the lattice extension in each of the D dimensions, which we bound, the uniformity is degraded due to finite support operators which wind around the system. We also outline how to achieve larger m values using quasi-D-dimensional cluster states. This opens the possibility to use cluster states to benchmark errors on quantum computers. We demonstrate this ability on a superconducting quantum computer, focusing on the one-dimensional cluster state, which, as we show, allows us to detect and identify one-qubit errors, distinguishing X, Y, and Z errors.
UR - http://www.scopus.com/inward/record.url?scp=85169293558&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.108.022426
DO - 10.1103/PhysRevA.108.022426
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AN - SCOPUS:85169293558
SN - 2469-9926
VL - 108
JO - Physical Review A
JF - Physical Review A
IS - 2
M1 - 022426
ER -